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In a survey of 150 people, 90 like tea, 60 like coffee, and 30 like both. How ma

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Question: In a survey of 150 people, 90 like tea, 60 like coffee, and 30 like both. How many people like neither tea nor coffee?

Options:

  1. 30
  2. 60
  3. 90
  4. 120

Correct Answer: 60

Solution: 

Using inclusion-exclusion, the number of people who like either tea or coffee is 90 + 60 - 30 = 120. Therefore, those who like neither is 150 - 120 = 30.

In a survey of 150 people, 90 like tea, 60 like coffee, and 30 like both. How ma

Practice Questions

Q1
In a survey of 150 people, 90 like tea, 60 like coffee, and 30 like both. How many people like neither tea nor coffee?
  1. 30
  2. 60
  3. 90
  4. 120

Questions & Step-by-Step Solutions

In a survey of 150 people, 90 like tea, 60 like coffee, and 30 like both. How many people like neither tea nor coffee?
  • Step 1: Identify the total number of people surveyed, which is 150.
  • Step 2: Identify how many people like tea, which is 90.
  • Step 3: Identify how many people like coffee, which is 60.
  • Step 4: Identify how many people like both tea and coffee, which is 30.
  • Step 5: Use the inclusion-exclusion principle to find the number of people who like either tea or coffee. This is calculated as: 90 (tea) + 60 (coffee) - 30 (both) = 120.
  • Step 6: To find the number of people who like neither tea nor coffee, subtract the number of people who like either from the total number of people surveyed: 150 - 120 = 30.
  • Inclusion-Exclusion Principle – A method used to calculate the size of the union of two sets by subtracting the size of their intersection from the sum of their individual sizes.
  • Set Theory – Understanding how to categorize and count elements in different groups, particularly in relation to overlapping groups.
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